Biostatistical Methods I - Final Project Code
Ravi Brenner, Cameron Chesbrough, Joe LaRocca, Wayne Monical
2024-12-10
Upload Data
proj_1_data = read_csv("data/Project_1_data.csv") |>
janitor::clean_names() |>
mutate(wkly_study_hours =
case_match(
wkly_study_hours,
"< 5" ~ "< 5 hours",
"10-May" ~ "5-10 hours",
"> 10" ~ "> 10 hours"
),
ethnic_group =
case_match(
ethnic_group,
"group A" ~ "A",
"group B" ~ "B",
"group C" ~ "C",
"group D" ~ "D",
"group E" ~ "E"
),
nr_siblings =
case_match(
nr_siblings,
0 ~ "0",
1 ~ "1",
2 ~ "2",
3 ~ "3",
4 ~ "4+",
5 ~ "4+",
6 ~ "4+",
7 ~ "4+"
)
) ## Rows: 948 Columns: 14
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (10): Gender, EthnicGroup, ParentEduc, LunchType, TestPrep, ParentMarita...
## dbl (4): NrSiblings, MathScore, ReadingScore, WritingScore
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.Filling NA’s. Creating Model Matrix
dummy_col_names = c(
"gender_male"
#, "gender_female"
# , "ethnic_group_A",
, "ethnic_group_B", "ethnic_group_C" , "ethnic_group_D" , "ethnic_group_E"
# , "parent_educ_some high school"
, "parent_educ_high school", "parent_educ_some college"
, "parent_educ_associate's degree", "parent_educ_bachelor's degree"
, "parent_educ_master's degree"
# , "lunch_type_standard"
,"lunch_type_free/reduced"
# , "test_prep_none"
, "test_prep_completed"
# , "parent_marital_status_married"
, "parent_marital_status_divorced", "parent_marital_status_single"
, "parent_marital_status_widowed"
# , "practice_sport_never"
, "practice_sport_sometimes", "practice_sport_regularly"
# , "is_first_child_no"
, "is_first_child_yes"
# , "transport_means_school_bus"
, "transport_means_private"
# , "nr_siblings_0"
, "nr_siblings_1", "nr_siblings_2", "nr_siblings_3", "nr_siblings_4+"
# , "wkly_study_hours_< 5 hours"
, "wkly_study_hours_> 10 hours", "wkly_study_hours_5-10 hours"
)
score_dummies =
proj_1_data %>%
dplyr::select(-math_score, -reading_score, -writing_score) %>%
dummy_cols(ignore_na = TRUE) %>%
dplyr::select(all_of(dummy_col_names)) %>%
## fill NA's
lapply(function(x) ifelse(is.na(x), round(mean(x, na.rm = TRUE), 3), x)) %>%
as.data.frame()Correlation
cor_df =
proj_1_data %>%
dplyr::select(-reading_score, -writing_score) %>%
drop_na()
cor_df =
model.matrix(object = math_score ~ ., data = cor_df) %>%
cor() %>%
as.data.frame()## Warning in cor(.): the standard deviation is zerocor_df =
cor_df %>%
mutate(x_name = row.names(cor_df)) %>%
filter(x_name != '(Intercept)') %>%
dplyr::select(-'(Intercept)') %>%
pivot_longer(
gendermale:`wkly_study_hours5-10 hours`
, values_to = 'correlation'
, names_to = 'y_name'
) %>%
filter(
substr(x_name, 1, 6) != substr(y_name, 1, 6),
tolower(x_name) < tolower(y_name)
)Getting a histogram of the correlations between the variables.
hist(cor_df$correlation,
main = "Histogram of Correlations Between Predictors",
xlab = "Correlation Coefficient")
Getting the top correlations
cor_df %>%
arrange(desc(correlation)) %>%
mutate(correlation = round(correlation, digits = 3)) %>%
head(6) %>%
knitr::kable()| x_name | y_name | correlation |
|---|---|---|
| nr_siblings1 | parent_educmaster’s degree | 0.103 |
| ethnic_groupC | parent_marital_statusmarried | 0.101 |
| ethnic_groupE | nr_siblings3 | 0.084 |
| nr_siblings4+ | parent_educhigh school | 0.083 |
| parent_educhigh school | test_prepnone | 0.081 |
| gendermale | parent_educhigh school | 0.080 |
Create Table Summarizing Response Variables
proj_1_data |>
dplyr::select(math_score, reading_score, writing_score) |>
pivot_longer(
cols= everything(),
names_to = "Test",
values_to = "Score"
) |>
group_by(Test) |>
summarize(Mean = round(mean(Score), 2),
StDev = round(sd(Score), 2),
Min = min(Score),
Max = max(Score)) |>
mutate(Test = case_match(
Test,
"math_score" ~ "Math",
"reading_score" ~ "Reading",
"writing_score" ~ "Writing"
)
) |>
knitr::kable()| Test | Mean | StDev | Min | Max |
|---|---|---|---|---|
| Math | 65.98 | 15.53 | 0 | 100 |
| Reading | 68.84 | 14.80 | 17 | 100 |
| Writing | 67.93 | 15.41 | 10 | 100 |
Single-Variable Categorical Plots
Ethnic Group
proj_1_data |>
ggplot(aes(x = ethnic_group)) +
geom_bar()
Parent Education
proj_1_data |>
ggplot(aes(x = parent_educ)) +
geom_bar()
Lunch Type
proj_1_data |>
ggplot(aes(x = lunch_type)) +
geom_bar()
Test Prep
proj_1_data |>
ggplot(aes(x = test_prep)) +
geom_bar()
Parent Marital Status
proj_1_data |>
ggplot(aes(x = parent_marital_status)) +
geom_bar()
Practicing Sports
proj_1_data |>
ggplot(aes(x = practice_sport)) +
geom_bar()
First Child
proj_1_data |>
ggplot(aes(x = is_first_child)) +
geom_bar()
Number of Siblings
proj_1_data |>
ggplot(aes(x = nr_siblings)) +
geom_bar()
Further EDA
# Histograms for Response Variables
ggplot(data=proj_1_data, aes(math_score)) +
geom_histogram(color = "black", fill = "white") +
labs(title = "Histogram of Math Scores",
x = "Math Score",
y = "") +
theme_bw()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
ggplot(data=proj_1_data, aes(reading_score)) +
geom_histogram(color = "black", fill = "white") +
labs(title = "Histogram of Reading Scores",
x = "Reading Score",
y = "") +
theme_bw()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
ggplot(data=proj_1_data, aes(writing_score)) +
geom_histogram(color = "black", fill = "white") +
labs(title = "Histogram of Writing Scores",
x = "Writing Score",
y = "") +
theme_bw()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
# Boxplots for Predictive Variables
ggplot(data=proj_1_data, aes(x=parent_educ,y=math_score)) +
geom_boxplot() +
labs(title = "Boxplots for Parent Education",
x = "Parent Level of Education",
y = "Math Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=parent_educ,y=reading_score)) +
geom_boxplot() +
labs(title = "Boxplots for Parent Education",
x = "Parent Level of Education",
y = "Reading Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=parent_educ,y=writing_score)) +
geom_boxplot() +
labs(title = "Boxplots for Parent Education",
x = "Parent Level of Education",
y = "Writng Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=wkly_study_hours,y=math_score)) +
geom_boxplot() +
labs(title = "Boxplots for Study Hours",
x = "Amount of Hours Studied",
y = "Math Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=wkly_study_hours,y=reading_score)) +
geom_boxplot() +
labs(title = "Boxplots for Study Hours",
x = "Amount of Hours Studied",
y = "Reading Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=wkly_study_hours,y=writing_score)) +
geom_boxplot() +
labs(title = "Boxplots for Study Hours",
x = "Amount of Hours Studied",
y = "Writing Score") +
theme_bw()
# Looks strong
ggplot(data=proj_1_data, aes(x=lunch_type,y=math_score)) +
geom_boxplot() +
labs(title = "Boxplots for Lunch Type",
x = "Lunch Type",
y = "Math Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=lunch_type,y=reading_score)) +
geom_boxplot() +
labs(title = "Boxplots for Lunch Type",
x = "Lunch Type",
y = "Reading Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=lunch_type,y=writing_score)) +
geom_boxplot() +
labs(title = "Boxplots for Lunch Type",
x = "Lunch Type",
y = "Writing Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=transport_means,y=math_score)) +
geom_boxplot() +
labs(title = "Boxplots for Transportation",
x = "Transportation Type",
y = "Math Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=transport_means,y=reading_score)) +
geom_boxplot() +
labs(title = "Boxplots for Transportation",
x = "Transportation Type",
y = "Reading Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=transport_means,y=writing_score)) +
geom_boxplot() +
labs(title = "Boxplots for Transportation",
x = "Transportation Type",
y = "Writing Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=practice_sport,y=math_score)) +
geom_boxplot() +
labs(title = "Boxplots for Sports",
x = "Sports Participation",
y = "Math Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=practice_sport,y=reading_score)) +
geom_boxplot() +
labs(title = "Boxplots for Sports",
x = "Sports Participation",
y = "Reading Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=practice_sport,y=writing_score)) +
geom_boxplot() +
labs(title = "Boxplots for Sports",
x = "Sports Participation",
y = "Writing Score") +
theme_bw()
# Looks strong, look at diff between math and read/write
ggplot(data=proj_1_data, aes(x=gender,y=math_score)) +
geom_boxplot() +
labs(title = "Boxplots for Gender",
x = "Gender",
y = "Math Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=gender,y=reading_score)) +
geom_boxplot() +
labs(title = "Boxplots for Gender",
x = "Gender",
y = "Reading Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=gender,y=writing_score)) +
geom_boxplot() +
labs(title = "Boxplots for Gender",
x = "Gender",
y = "Writing Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=ethnic_group,y=math_score)) +
geom_boxplot() +
labs(title = "Boxplots for Ethnic Group",
x = "Ethnic Group",
y = "Math Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=ethnic_group,y=reading_score)) +
geom_boxplot() +
labs(title = "Boxplots for Ethnic Group",
x = "Ethnic Group",
y = "Reading Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=ethnic_group,y=writing_score)) +
geom_boxplot() +
labs(title = "Boxplots for Ethnic Group",
x = "Ethnic Group",
y = "Writing Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=parent_marital_status,y=math_score)) +
geom_boxplot() +
labs(title = "Boxplots for Parental Marital Status",
x = "Parental Marital Status",
y = "Math Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=parent_marital_status,y=reading_score)) +
geom_boxplot() +
labs(title = "Boxplots for Parental Marital Status",
x = "Parental Marital Status",
y = "Reading Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=parent_marital_status,y=writing_score)) +
geom_boxplot() +
labs(title = "Boxplots for Parental Marital Status",
x = "Parental Marital Status",
y = "Writing Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=is_first_child,y=math_score)) +
geom_boxplot() +
labs(title = "Boxplots for First Child Status",
x = "First Child Status",
y = "Math Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=is_first_child,y=reading_score)) +
geom_boxplot() +
labs(title = "Boxplots for First Child Status",
x = "First Child Status",
y = "Reading Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=is_first_child,y=writing_score)) +
geom_boxplot() +
labs(title = "Boxplots for First Child Status",
x = "First Child Status",
y = "Writing Score") +
theme_bw()
ggplot(data=proj_1_data, aes(x=nr_siblings,y=math_score)) + geom_point()
ggplot(data=proj_1_data, aes(x=nr_siblings,y=reading_score)) + geom_point()
ggplot(data=proj_1_data, aes(x=nr_siblings,y=writing_score)) + geom_point()
Modeling
Create Data Frames with only Math, Reading, Writing to Make LM Functions Easier to Write
math_data = score_dummies |>
mutate(math_score = proj_1_data$math_score)
reading_data = score_dummies |>
mutate(reading_score = proj_1_data$reading_score)
writing_data = score_dummies |>
mutate(writing_score = proj_1_data$writing_score)All Predictors
Math_All
lm_all_math = lm(math_score ~ ., data = math_data)
summary(lm_all_math)##
## Call:
## lm(formula = math_score ~ ., data = math_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -51.644 -8.793 0.423 9.511 32.139
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 55.3291 2.8758 19.240 < 2e-16 ***
## gender_male 4.9630 0.8757 5.667 1.94e-08 ***
## ethnic_group_B 1.2761 1.8230 0.700 0.484113
## ethnic_group_C 0.9979 1.7119 0.583 0.560079
## ethnic_group_D 4.9448 1.7341 2.852 0.004448 **
## ethnic_group_E 9.6236 1.9327 4.979 7.61e-07 ***
## parent_educ_high.school -0.5837 1.4672 -0.398 0.690828
## parent_educ_some.college 3.8182 1.4197 2.689 0.007288 **
## parent_educ_associate.s.degree 4.6864 1.4237 3.292 0.001033 **
## parent_educ_bachelor.s.degree 6.0301 1.6819 3.585 0.000354 ***
## parent_educ_master.s.degree 7.7549 2.1044 3.685 0.000242 ***
## lunch_type_free.reduced -11.1535 0.9133 -12.212 < 2e-16 ***
## test_prep_completed 5.6331 0.9380 6.006 2.74e-09 ***
## parent_marital_status_divorced -4.0782 1.2617 -3.232 0.001271 **
## parent_marital_status_single -2.9959 1.0923 -2.743 0.006210 **
## parent_marital_status_widowed 0.4294 2.8111 0.153 0.878615
## practice_sport_sometimes 2.2097 1.4131 1.564 0.118225
## practice_sport_regularly 3.3317 1.4652 2.274 0.023204 *
## is_first_child_yes 2.2742 0.9669 2.352 0.018884 *
## transport_means_private -0.6603 0.9447 -0.699 0.484751
## nr_siblings_1 -1.4314 1.6328 -0.877 0.380910
## nr_siblings_2 -1.0911 1.6758 -0.651 0.515145
## nr_siblings_3 0.1220 1.6846 0.072 0.942264
## nr_siblings_4. -0.0567 1.7796 -0.032 0.974590
## wkly_study_hours_..10.hours 3.7385 1.3937 2.682 0.007441 **
## wkly_study_hours_5.10.hours 3.0963 1.0352 2.991 0.002854 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.29 on 922 degrees of freedom
## Multiple R-squared: 0.2867, Adjusted R-squared: 0.2674
## F-statistic: 14.82 on 25 and 922 DF, p-value: < 2.2e-16aic_all_math = AIC(lm_all_math)
bic_all_math = BIC(lm_all_math)
adjr2_all_math = lm_all_math |> broom::glance() |> dplyr::select(adj.r.squared)Reading_All
lm_all_reading = lm(reading_score ~ ., data = reading_data)
summary(lm_all_reading)##
## Call:
## lm(formula = reading_score ~ ., data = reading_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -44.457 -8.817 0.626 8.999 30.733
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 65.88422 2.81201 23.430 < 2e-16 ***
## gender_male -7.24074 0.85629 -8.456 < 2e-16 ***
## ethnic_group_B 0.30125 1.78258 0.169 0.865835
## ethnic_group_C 0.71554 1.67395 0.427 0.669146
## ethnic_group_D 3.58680 1.69563 2.115 0.034670 *
## ethnic_group_E 5.03278 1.88985 2.663 0.007878 **
## parent_educ_high.school -0.92297 1.43463 -0.643 0.520158
## parent_educ_some.college 2.71841 1.38824 1.958 0.050512 .
## parent_educ_associate.s.degree 4.32882 1.39213 3.109 0.001932 **
## parent_educ_bachelor.s.degree 5.77552 1.64460 3.512 0.000467 ***
## parent_educ_master.s.degree 9.23894 2.05769 4.490 8.03e-06 ***
## lunch_type_free.reduced -7.52265 0.89309 -8.423 < 2e-16 ***
## test_prep_completed 7.04256 0.91718 7.678 4.10e-14 ***
## parent_marital_status_divorced -4.26487 1.23371 -3.457 0.000571 ***
## parent_marital_status_single -3.01973 1.06807 -2.827 0.004796 **
## parent_marital_status_widowed -0.02568 2.74877 -0.009 0.992549
## practice_sport_sometimes 0.95187 1.38176 0.689 0.491068
## practice_sport_regularly 0.60546 1.43276 0.423 0.672695
## is_first_child_yes 2.45298 0.94548 2.594 0.009625 **
## transport_means_private -1.33099 0.92376 -1.441 0.149970
## nr_siblings_1 0.41222 1.59661 0.258 0.796325
## nr_siblings_2 -0.54501 1.63861 -0.333 0.739506
## nr_siblings_3 0.26754 1.64727 0.162 0.871017
## nr_siblings_4. 0.02602 1.74014 0.015 0.988071
## wkly_study_hours_..10.hours 2.07394 1.36281 1.522 0.128400
## wkly_study_hours_5.10.hours 2.20047 1.01222 2.174 0.029966 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13 on 922 degrees of freedom
## Multiple R-squared: 0.249, Adjusted R-squared: 0.2286
## F-statistic: 12.23 on 25 and 922 DF, p-value: < 2.2e-16aic_all_reading = AIC(lm_all_reading)
bic_all_reading = BIC(lm_all_reading)
adjr2_all_reading = lm_all_reading |> broom::glance() |> dplyr::select(adj.r.squared)Writing_All
lm_all_writing = lm(writing_score ~ ., data = writing_data)
summary(lm_all_writing)##
## Call:
## lm(formula = writing_score ~ ., data = writing_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -49.142 -8.440 1.013 9.108 29.304
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 62.92757 2.73423 23.015 < 2e-16 ***
## gender_male -9.20011 0.83260 -11.050 < 2e-16 ***
## ethnic_group_B 0.18122 1.73328 0.105 0.916752
## ethnic_group_C 0.82358 1.62765 0.506 0.612983
## ethnic_group_D 5.54795 1.64874 3.365 0.000797 ***
## ethnic_group_E 4.60536 1.83758 2.506 0.012375 *
## parent_educ_high.school -0.59051 1.39495 -0.423 0.672161
## parent_educ_some.college 4.38234 1.34985 3.247 0.001210 **
## parent_educ_associate.s.degree 5.52787 1.35363 4.084 4.82e-05 ***
## parent_educ_bachelor.s.degree 8.12925 1.59911 5.084 4.48e-07 ***
## parent_educ_master.s.degree 11.99941 2.00078 5.997 2.88e-09 ***
## lunch_type_free.reduced -8.39668 0.86839 -9.669 < 2e-16 ***
## test_prep_completed 9.75707 0.89181 10.941 < 2e-16 ***
## parent_marital_status_divorced -4.36455 1.19959 -3.638 0.000290 ***
## parent_marital_status_single -3.33754 1.03853 -3.214 0.001356 **
## parent_marital_status_widowed -0.94821 2.67275 -0.355 0.722843
## practice_sport_sometimes 2.20441 1.34354 1.641 0.101191
## practice_sport_regularly 2.92713 1.39313 2.101 0.035902 *
## is_first_child_yes 2.07416 0.91933 2.256 0.024294 *
## transport_means_private -1.15980 0.89821 -1.291 0.196947
## nr_siblings_1 -0.62574 1.55246 -0.403 0.686992
## nr_siblings_2 -1.20213 1.59329 -0.754 0.450744
## nr_siblings_3 0.09188 1.60171 0.057 0.954267
## nr_siblings_4. -0.03309 1.69201 -0.020 0.984400
## wkly_study_hours_..10.hours 2.03234 1.32512 1.534 0.125445
## wkly_study_hours_5.10.hours 2.19602 0.98423 2.231 0.025907 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.64 on 922 degrees of freedom
## Multiple R-squared: 0.3453, Adjusted R-squared: 0.3275
## F-statistic: 19.45 on 25 and 922 DF, p-value: < 2.2e-16aic_all_writing = AIC(lm_all_writing)
bic_all_writing = BIC(lm_all_writing)
adjr2_all_writing = lm_all_writing |> broom::glance() |> dplyr::select(adj.r.squared)Economic Model
Math_Econ
lm_econ_math = lm(math_score ~ parent_educ_high.school +
parent_educ_some.college +
parent_educ_associate.s.degree +
parent_educ_bachelor.s.degree +
parent_educ_master.s.degree +
lunch_type_free.reduced +
test_prep_completed + transport_means_private,
data = math_data)
summary(lm_econ_math)##
## Call:
## lm(formula = math_score ~ parent_educ_high.school + parent_educ_some.college +
## parent_educ_associate.s.degree + parent_educ_bachelor.s.degree +
## parent_educ_master.s.degree + lunch_type_free.reduced + test_prep_completed +
## transport_means_private, data = math_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -52.868 -9.768 0.369 10.286 36.290
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 64.5844 1.2743 50.682 < 2e-16 ***
## parent_educ_high.school 0.1994 1.5326 0.130 0.896529
## parent_educ_some.college 4.8978 1.4841 3.300 0.001003 **
## parent_educ_associate.s.degree 5.5171 1.4855 3.714 0.000216 ***
## parent_educ_bachelor.s.degree 6.6969 1.7600 3.805 0.000151 ***
## parent_educ_master.s.degree 7.7135 2.1893 3.523 0.000447 ***
## lunch_type_free.reduced -11.7166 0.9558 -12.258 < 2e-16 ***
## test_prep_completed 6.1758 0.9822 6.288 4.93e-10 ***
## transport_means_private -0.8511 0.9899 -0.860 0.390107
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.02 on 939 degrees of freedom
## Multiple R-squared: 0.1922, Adjusted R-squared: 0.1853
## F-statistic: 27.93 on 8 and 939 DF, p-value: < 2.2e-16aic_econ_math = AIC(lm_econ_math)
bic_econ_math = BIC(lm_econ_math)
adjr2_econ_math = lm_econ_math |> broom::glance() |> dplyr::select(adj.r.squared)Reading_Econ
lm_econ_reading = lm(reading_score ~ parent_educ_high.school +
parent_educ_some.college +
parent_educ_associate.s.degree +
parent_educ_bachelor.s.degree +
parent_educ_master.s.degree +
lunch_type_free.reduced +
test_prep_completed + transport_means_private,
data = reading_data)
summary(lm_econ_reading)##
## Call:
## lm(formula = reading_score ~ parent_educ_high.school + parent_educ_some.college +
## parent_educ_associate.s.degree + parent_educ_bachelor.s.degree +
## parent_educ_master.s.degree + lunch_type_free.reduced + test_prep_completed +
## transport_means_private, data = reading_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -41.982 -8.633 0.076 9.479 33.631
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 66.5480 1.2423 53.569 < 2e-16 ***
## parent_educ_high.school -1.0197 1.4940 -0.683 0.495087
## parent_educ_some.college 3.5454 1.4468 2.450 0.014448 *
## parent_educ_associate.s.degree 4.5881 1.4481 3.168 0.001583 **
## parent_educ_bachelor.s.degree 6.5793 1.7158 3.835 0.000134 ***
## parent_educ_master.s.degree 10.4679 2.1343 4.905 1.10e-06 ***
## lunch_type_free.reduced -7.5664 0.9318 -8.120 1.46e-15 ***
## test_prep_completed 7.0994 0.9575 7.414 2.73e-13 ***
## transport_means_private -1.5933 0.9650 -1.651 0.099059 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.67 on 939 degrees of freedom
## Multiple R-squared: 0.1546, Adjusted R-squared: 0.1474
## F-statistic: 21.47 on 8 and 939 DF, p-value: < 2.2e-16aic_econ_reading = AIC(lm_econ_reading)
bic_econ_reading = BIC(lm_econ_reading)
adjr2_econ_reading = lm_econ_reading |> broom::glance() |> dplyr::select(adj.r.squared)Writing_Econ
lm_econ_writing = lm(writing_score ~ parent_educ_high.school +
parent_educ_some.college +
parent_educ_associate.s.degree +
parent_educ_bachelor.s.degree +
parent_educ_master.s.degree +
lunch_type_free.reduced +
test_prep_completed + transport_means_private,
data = writing_data)
summary(lm_econ_writing)##
## Call:
## lm(formula = writing_score ~ parent_educ_high.school + parent_educ_some.college +
## parent_educ_associate.s.degree + parent_educ_bachelor.s.degree +
## parent_educ_master.s.degree + lunch_type_free.reduced + test_prep_completed +
## transport_means_private, data = writing_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -45.507 -8.836 0.288 9.665 30.589
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 63.7929 1.2466 51.175 < 2e-16 ***
## parent_educ_high.school -0.8257 1.4992 -0.551 0.581910
## parent_educ_some.college 5.2478 1.4518 3.615 0.000317 ***
## parent_educ_associate.s.degree 5.6176 1.4531 3.866 0.000118 ***
## parent_educ_bachelor.s.degree 8.9190 1.7217 5.180 2.71e-07 ***
## parent_educ_master.s.degree 13.0360 2.1416 6.087 1.67e-09 ***
## lunch_type_free.reduced -8.2864 0.9350 -8.862 < 2e-16 ***
## test_prep_completed 9.7026 0.9608 10.098 < 2e-16 ***
## transport_means_private -1.3891 0.9683 -1.435 0.151748
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.71 on 939 degrees of freedom
## Multiple R-squared: 0.2152, Adjusted R-squared: 0.2085
## F-statistic: 32.18 on 8 and 939 DF, p-value: < 2.2e-16aic_econ_writing = AIC(lm_econ_writing)
bic_econ_writing = BIC(lm_econ_writing)
adjr2_econ_writing = lm_econ_writing |> broom::glance() |> dplyr::select(adj.r.squared)Hard Worker Model
Math_HW
lm_hw_math = lm(math_score ~ wkly_study_hours_..10.hours +
wkly_study_hours_5.10.hours +
practice_sport_sometimes +
practice_sport_regularly,
data = math_data)
summary(lm_hw_math)##
## Call:
## lm(formula = math_score ~ wkly_study_hours_..10.hours + wkly_study_hours_5.10.hours +
## practice_sport_sometimes + practice_sport_regularly, data = math_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -68.805 -9.809 0.144 10.511 35.156
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 62.1732 1.6655 37.329 < 2e-16 ***
## wkly_study_hours_..10.hours 4.9610 1.5929 3.114 0.00190 **
## wkly_study_hours_5.10.hours 3.6363 1.1888 3.059 0.00229 **
## practice_sport_sometimes 0.6823 1.6231 0.420 0.67430
## practice_sport_regularly 1.6711 1.6820 0.993 0.32073
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.45 on 943 degrees of freedom
## Multiple R-squared: 0.01472, Adjusted R-squared: 0.01054
## F-statistic: 3.521 on 4 and 943 DF, p-value: 0.007313aic_hw_math = AIC(lm_hw_math)
bic_hw_math = BIC(lm_hw_math)
adjr2_hw_math = lm_hw_math |> broom::glance() |> dplyr::select(adj.r.squared)Reading_HW
lm_hw_reading = lm(reading_score ~ wkly_study_hours_..10.hours +
wkly_study_hours_5.10.hours +
practice_sport_sometimes +
practice_sport_regularly,
data = reading_data)
summary(lm_hw_reading)##
## Call:
## lm(formula = reading_score ~ wkly_study_hours_..10.hours + wkly_study_hours_5.10.hours +
## practice_sport_sometimes + practice_sport_regularly, data = reading_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -52.350 -9.874 0.869 10.192 32.585
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 67.136978 1.593235 42.139 <2e-16 ***
## wkly_study_hours_..10.hours 2.934960 1.523746 1.926 0.0544 .
## wkly_study_hours_5.10.hours 2.672754 1.137214 2.350 0.0190 *
## practice_sport_sometimes -0.006351 1.552645 -0.004 0.9967
## practice_sport_regularly -0.721940 1.608993 -0.449 0.6538
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.78 on 943 degrees of freedom
## Multiple R-squared: 0.007176, Adjusted R-squared: 0.002965
## F-statistic: 1.704 on 4 and 943 DF, p-value: 0.1469aic_hw_reading = AIC(lm_hw_reading)
bic_hw_reading = BIC(lm_hw_reading)
adjr2_hw_reading = lm_hw_reading |> broom::glance() |> dplyr::select(adj.r.squared)Writing_HW
lm_hw_writing = lm(writing_score ~ wkly_study_hours_..10.hours +
wkly_study_hours_5.10.hours +
practice_sport_sometimes +
practice_sport_regularly,
data = writing_data)
summary(lm_hw_writing)##
## Call:
## lm(formula = writing_score ~ wkly_study_hours_..10.hours + wkly_study_hours_5.10.hours +
## practice_sport_sometimes + practice_sport_regularly, data = writing_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -59.297 -10.728 0.877 10.680 33.829
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 64.589 1.659 38.936 <2e-16 ***
## wkly_study_hours_..10.hours 3.126 1.587 1.971 0.0491 *
## wkly_study_hours_5.10.hours 2.731 1.184 2.307 0.0213 *
## practice_sport_sometimes 1.408 1.617 0.871 0.3840
## practice_sport_regularly 1.582 1.675 0.945 0.3451
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.39 on 943 degrees of freedom
## Multiple R-squared: 0.007621, Adjusted R-squared: 0.003412
## F-statistic: 1.81 on 4 and 943 DF, p-value: 0.1246aic_hw_writing = AIC(lm_hw_writing)
bic_hw_writing = BIC(lm_hw_writing)
adjr2_hw_writing = lm_hw_writing |> broom::glance() |> dplyr::select(adj.r.squared)Demographic Model
Math_Demo
lm_demo_math = lm(math_score ~ gender_male +
ethnic_group_B +
ethnic_group_C +
ethnic_group_D +
ethnic_group_E, data = math_data)
summary(lm_demo_math)##
## Call:
## lm(formula = math_score ~ gender_male + ethnic_group_B + ethnic_group_C +
## ethnic_group_D + ethnic_group_E, data = math_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -61.526 -9.336 0.474 10.474 35.196
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 58.9959 1.7638 33.449 < 2e-16 ***
## gender_male 5.3481 0.9736 5.493 5.08e-08 ***
## ethnic_group_B 1.8086 2.0254 0.893 0.37211
## ethnic_group_C 2.5305 1.9007 1.331 0.18340
## ethnic_group_D 5.7866 1.9317 2.996 0.00281 **
## ethnic_group_E 12.2760 2.1425 5.730 1.35e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.92 on 942 degrees of freedom
## Multiple R-squared: 0.08164, Adjusted R-squared: 0.07677
## F-statistic: 16.75 on 5 and 942 DF, p-value: 7.063e-16aic_demo_math = AIC(lm_demo_math)
bic_demo_math = BIC(lm_demo_math)
adjr2_demo_math = lm_demo_math |> broom::glance() |> dplyr::select(adj.r.squared)Reading_Demo
lm_demo_reading = lm(reading_score ~ gender_male +
ethnic_group_B +
ethnic_group_C +
ethnic_group_D +
ethnic_group_E, data = reading_data)
summary(lm_demo_reading)##
## Call:
## lm(formula = reading_score ~ gender_male + ethnic_group_B + ethnic_group_C +
## ethnic_group_D + ethnic_group_E, data = reading_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -54.363 -9.406 0.538 10.512 33.693
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 69.4620 1.6847 41.231 < 2e-16 ***
## gender_male -7.0560 0.9299 -7.588 7.82e-14 ***
## ethnic_group_B 0.6951 1.9346 0.359 0.719464
## ethnic_group_C 1.9009 1.8155 1.047 0.295355
## ethnic_group_D 4.0816 1.8451 2.212 0.027198 *
## ethnic_group_E 7.0939 2.0465 3.466 0.000551 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.25 on 942 degrees of freedom
## Multiple R-squared: 0.07732, Adjusted R-squared: 0.07242
## F-statistic: 15.79 on 5 and 942 DF, p-value: 5.975e-15aic_demo_reading = AIC(lm_demo_reading)
bic_demo_reading = BIC(lm_demo_reading)
adjr2_demo_reading = lm_demo_reading |> broom::glance() |> dplyr::select(adj.r.squared)Writing_Demo
lm_demo_writing = lm(writing_score ~ gender_male +
ethnic_group_B +
ethnic_group_C +
ethnic_group_D +
ethnic_group_E, data = writing_data)
summary(lm_demo_writing)##
## Call:
## lm(formula = writing_score ~ gender_male + ethnic_group_B + ethnic_group_C +
## ethnic_group_D + ethnic_group_E, data = writing_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -61.073 -9.286 0.703 9.886 32.953
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 68.7161 1.7213 39.922 < 2e-16 ***
## gender_male -8.9584 0.9501 -9.429 < 2e-16 ***
## ethnic_group_B 0.6785 1.9766 0.343 0.731471
## ethnic_group_C 2.3567 1.8549 1.271 0.204220
## ethnic_group_D 6.2968 1.8851 3.340 0.000870 ***
## ethnic_group_E 7.2890 2.0909 3.486 0.000513 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.56 on 942 degrees of freedom
## Multiple R-squared: 0.1119, Adjusted R-squared: 0.1072
## F-statistic: 23.75 on 5 and 942 DF, p-value: < 2.2e-16aic_demo_writing = AIC(lm_demo_writing)
bic_demo_writing = BIC(lm_demo_writing)
adjr2_demo_writing = lm_demo_writing |> broom::glance() |> dplyr::select(adj.r.squared)Family Structure Model
Math_Fam
lm_fam_math = lm(math_score ~ parent_marital_status_divorced +
parent_marital_status_single +
parent_marital_status_widowed +
is_first_child_yes +
nr_siblings_1 +
nr_siblings_2 +
nr_siblings_3 +
nr_siblings_4.,
data = math_data)
summary(lm_fam_math)##
## Call:
## lm(formula = math_score ~ parent_marital_status_divorced + parent_marital_status_single +
## parent_marital_status_widowed + is_first_child_yes + nr_siblings_1 +
## nr_siblings_2 + nr_siblings_3 + nr_siblings_4., data = math_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -65.822 -9.958 0.077 10.859 36.096
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 68.2938 1.9139 35.682 < 2e-16 ***
## parent_marital_status_divorced -4.7421 1.4493 -3.272 0.00111 **
## parent_marital_status_single -3.2902 1.2554 -2.621 0.00891 **
## parent_marital_status_widowed 0.3985 3.2269 0.124 0.90173
## is_first_child_yes 1.9176 1.1098 1.728 0.08435 .
## nr_siblings_1 -2.9968 1.8624 -1.609 0.10793
## nr_siblings_2 -3.1529 1.9164 -1.645 0.10026
## nr_siblings_3 -1.0994 1.9321 -0.569 0.56949
## nr_siblings_4. -1.4586 2.0383 -0.716 0.47441
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.41 on 939 degrees of freedom
## Multiple R-squared: 0.02401, Adjusted R-squared: 0.01569
## F-statistic: 2.887 on 8 and 939 DF, p-value: 0.003506aic_fam_math = AIC(lm_fam_math)
bic_fam_math = BIC(lm_fam_math)
adjr2_fam_math = lm_fam_math |> broom::glance() |> dplyr::select(adj.r.squared)Reading_Fam
lm_fam_reading = lm(reading_score ~ parent_marital_status_divorced +
parent_marital_status_single +
parent_marital_status_widowed +
is_first_child_yes +
nr_siblings_1 +
nr_siblings_2 +
nr_siblings_3 +
nr_siblings_4.,
data = reading_data)
summary(lm_fam_reading)##
## Call:
## lm(formula = reading_score ~ parent_marital_status_divorced +
## parent_marital_status_single + parent_marital_status_widowed +
## is_first_child_yes + nr_siblings_1 + nr_siblings_2 + nr_siblings_3 +
## nr_siblings_4., data = reading_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -52.37 -10.33 0.70 10.30 33.99
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 67.4458727 1.8249531 36.958 < 2e-16 ***
## parent_marital_status_divorced -4.5553597 1.3818853 -3.296 0.00102 **
## parent_marital_status_single -2.4613325 1.1970580 -2.056 0.04004 *
## parent_marital_status_widowed 0.0004839 3.0768811 0.000 0.99987
## is_first_child_yes 3.1206673 1.0582215 2.949 0.00327 **
## nr_siblings_1 1.2360917 1.7758246 0.696 0.48656
## nr_siblings_2 -0.2959273 1.8273200 -0.162 0.87138
## nr_siblings_3 1.2615396 1.8422516 0.685 0.49365
## nr_siblings_4. 0.7630319 1.9435692 0.393 0.69471
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.69 on 939 degrees of freedom
## Multiple R-squared: 0.02287, Adjusted R-squared: 0.01454
## F-statistic: 2.747 on 8 and 939 DF, p-value: 0.005314aic_fam_reading = AIC(lm_fam_reading)
bic_fam_reading = BIC(lm_fam_reading)
adjr2_fam_reading = lm_fam_reading |> broom::glance() |> dplyr::select(adj.r.squared)Writing_Fam
lm_fam_writing = lm(writing_score ~ parent_marital_status_divorced +
parent_marital_status_single +
parent_marital_status_widowed +
is_first_child_yes +
nr_siblings_1 +
nr_siblings_2 +
nr_siblings_3 +
nr_siblings_4.,
data = writing_data)
summary(lm_fam_writing)##
## Call:
## lm(formula = writing_score ~ parent_marital_status_divorced +
## parent_marital_status_single + parent_marital_status_widowed +
## is_first_child_yes + nr_siblings_1 + nr_siblings_2 + nr_siblings_3 +
## nr_siblings_4., data = writing_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -58.822 -10.838 0.763 10.796 34.742
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 67.0068 1.9021 35.228 < 2e-16 ***
## parent_marital_status_divorced -4.6811 1.4403 -3.250 0.00119 **
## parent_marital_status_single -2.4800 1.2477 -1.988 0.04713 *
## parent_marital_status_widowed -0.4628 3.2070 -0.144 0.88529
## is_first_child_yes 2.9327 1.1030 2.659 0.00797 **
## nr_siblings_1 0.3615 1.8509 0.195 0.84519
## nr_siblings_2 -0.7357 1.9046 -0.386 0.69939
## nr_siblings_3 1.3629 1.9201 0.710 0.47801
## nr_siblings_4. 0.8048 2.0257 0.397 0.69125
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.31 on 939 degrees of freedom
## Multiple R-squared: 0.02126, Adjusted R-squared: 0.01292
## F-statistic: 2.55 on 8 and 939 DF, p-value: 0.009457aic_fam_writing = AIC(lm_fam_writing)
bic_fam_writing = BIC(lm_fam_writing)
adjr2_fam_writing = lm_fam_writing |> broom::glance() |> dplyr::select(adj.r.squared)Backwards Selection
Math
lm_step_math = stepAIC(lm_all_math, direction = "backward")## Start: AIC=4931.05
## math_score ~ gender_male + ethnic_group_B + ethnic_group_C +
## ethnic_group_D + ethnic_group_E + parent_educ_high.school +
## parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + parent_marital_status_widowed +
## practice_sport_sometimes + practice_sport_regularly + is_first_child_yes +
## transport_means_private + nr_siblings_1 + nr_siblings_2 +
## nr_siblings_3 + nr_siblings_4. + wkly_study_hours_..10.hours +
## wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - nr_siblings_4. 1 0.2 162924 4929.1
## - nr_siblings_3 1 0.9 162924 4929.1
## - parent_marital_status_widowed 1 4.1 162928 4929.1
## - parent_educ_high.school 1 28.0 162951 4929.2
## - ethnic_group_C 1 60.0 162983 4929.4
## - nr_siblings_2 1 74.9 162998 4929.5
## - transport_means_private 1 86.3 163010 4929.6
## - ethnic_group_B 1 86.6 163010 4929.6
## - nr_siblings_1 1 135.8 163059 4929.8
## <none> 162923 4931.1
## - practice_sport_sometimes 1 432.1 163355 4931.6
## - practice_sport_regularly 1 913.6 163837 4934.4
## - is_first_child_yes 1 977.5 163901 4934.7
## - wkly_study_hours_..10.hours 1 1271.4 164195 4936.4
## - parent_educ_some.college 1 1278.1 164201 4936.5
## - parent_marital_status_single 1 1329.4 164253 4936.8
## - ethnic_group_D 1 1436.9 164360 4937.4
## - wkly_study_hours_5.10.hours 1 1580.9 164504 4938.2
## - parent_marital_status_divorced 1 1846.2 164770 4939.7
## - parent_educ_associate.s.degree 1 1914.7 164838 4940.1
## - parent_educ_bachelor.s.degree 1 2271.4 165195 4942.2
## - parent_educ_master.s.degree 1 2399.8 165323 4942.9
## - ethnic_group_E 1 4381.2 167305 4954.2
## - gender_male 1 5675.7 168599 4961.5
## - test_prep_completed 1 6373.3 169297 4965.4
## - lunch_type_free.reduced 1 26351.9 189275 5071.2
##
## Step: AIC=4929.05
## math_score ~ gender_male + ethnic_group_B + ethnic_group_C +
## ethnic_group_D + ethnic_group_E + parent_educ_high.school +
## parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + parent_marital_status_widowed +
## practice_sport_sometimes + practice_sport_regularly + is_first_child_yes +
## transport_means_private + nr_siblings_1 + nr_siblings_2 +
## nr_siblings_3 + wkly_study_hours_..10.hours + wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - nr_siblings_3 1 2.6 162926 4927.1
## - parent_marital_status_widowed 1 4.0 162928 4927.1
## - parent_educ_high.school 1 28.3 162952 4927.2
## - ethnic_group_C 1 60.2 162984 4927.4
## - transport_means_private 1 86.2 163010 4927.6
## - ethnic_group_B 1 86.8 163010 4927.6
## - nr_siblings_2 1 122.0 163046 4927.8
## - nr_siblings_1 1 231.3 163155 4928.4
## <none> 162924 4929.1
## - practice_sport_sometimes 1 433.0 163357 4929.6
## - practice_sport_regularly 1 916.0 163840 4932.4
## - is_first_child_yes 1 1024.4 163948 4933.0
## - wkly_study_hours_..10.hours 1 1277.0 164201 4934.5
## - parent_educ_some.college 1 1280.2 164204 4934.5
## - parent_marital_status_single 1 1330.6 164254 4934.8
## - ethnic_group_D 1 1440.0 164364 4935.4
## - wkly_study_hours_5.10.hours 1 1583.1 164507 4936.2
## - parent_marital_status_divorced 1 1846.1 164770 4937.7
## - parent_educ_associate.s.degree 1 1916.6 164840 4938.1
## - parent_educ_bachelor.s.degree 1 2271.5 165195 4940.2
## - parent_educ_master.s.degree 1 2402.9 165327 4940.9
## - ethnic_group_E 1 4386.6 167310 4952.2
## - gender_male 1 5713.1 168637 4959.7
## - test_prep_completed 1 6373.2 169297 4963.4
## - lunch_type_free.reduced 1 26390.1 189314 5069.4
##
## Step: AIC=4927.07
## math_score ~ gender_male + ethnic_group_B + ethnic_group_C +
## ethnic_group_D + ethnic_group_E + parent_educ_high.school +
## parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + parent_marital_status_widowed +
## practice_sport_sometimes + practice_sport_regularly + is_first_child_yes +
## transport_means_private + nr_siblings_1 + nr_siblings_2 +
## wkly_study_hours_..10.hours + wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - parent_marital_status_widowed 1 4.0 162930 4925.1
## - parent_educ_high.school 1 28.8 162955 4925.2
## - ethnic_group_C 1 60.8 162987 4925.4
## - transport_means_private 1 86.1 163012 4925.6
## - ethnic_group_B 1 88.1 163014 4925.6
## - nr_siblings_2 1 178.2 163104 4926.1
## - nr_siblings_1 1 332.3 163258 4927.0
## <none> 162926 4927.1
## - practice_sport_sometimes 1 432.5 163359 4927.6
## - practice_sport_regularly 1 915.7 163842 4930.4
## - is_first_child_yes 1 1028.5 163955 4931.0
## - wkly_study_hours_..10.hours 1 1281.8 164208 4932.5
## - parent_educ_some.college 1 1283.4 164210 4932.5
## - parent_marital_status_single 1 1329.3 164255 4932.8
## - ethnic_group_D 1 1443.8 164370 4933.4
## - wkly_study_hours_5.10.hours 1 1580.6 164507 4934.2
## - parent_marital_status_divorced 1 1843.5 164770 4935.7
## - parent_educ_associate.s.degree 1 1916.5 164843 4936.2
## - parent_educ_bachelor.s.degree 1 2275.5 165202 4938.2
## - parent_educ_master.s.degree 1 2409.5 165336 4939.0
## - ethnic_group_E 1 4390.0 167316 4950.3
## - gender_male 1 5712.9 168639 4957.7
## - test_prep_completed 1 6370.7 169297 4961.4
## - lunch_type_free.reduced 1 26387.6 189314 5067.4
##
## Step: AIC=4925.09
## math_score ~ gender_male + ethnic_group_B + ethnic_group_C +
## ethnic_group_D + ethnic_group_E + parent_educ_high.school +
## parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + practice_sport_sometimes +
## practice_sport_regularly + is_first_child_yes + transport_means_private +
## nr_siblings_1 + nr_siblings_2 + wkly_study_hours_..10.hours +
## wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - parent_educ_high.school 1 28.5 162959 4923.3
## - ethnic_group_C 1 62.0 162992 4923.5
## - transport_means_private 1 88.0 163018 4923.6
## - ethnic_group_B 1 90.8 163021 4923.6
## - nr_siblings_2 1 180.5 163111 4924.1
## - nr_siblings_1 1 334.1 163264 4925.0
## <none> 162930 4925.1
## - practice_sport_sometimes 1 430.2 163360 4925.6
## - practice_sport_regularly 1 917.9 163848 4928.4
## - is_first_child_yes 1 1030.3 163961 4929.1
## - wkly_study_hours_..10.hours 1 1284.0 164214 4930.5
## - parent_educ_some.college 1 1284.3 164214 4930.5
## - parent_marital_status_single 1 1362.9 164293 4931.0
## - ethnic_group_D 1 1453.5 164384 4931.5
## - wkly_study_hours_5.10.hours 1 1593.4 164524 4932.3
## - parent_marital_status_divorced 1 1879.0 164809 4934.0
## - parent_educ_associate.s.degree 1 1912.7 164843 4934.2
## - parent_educ_bachelor.s.degree 1 2275.5 165206 4936.2
## - parent_educ_master.s.degree 1 2414.9 165345 4937.0
## - ethnic_group_E 1 4393.2 167323 4948.3
## - gender_male 1 5713.7 168644 4955.8
## - test_prep_completed 1 6386.8 169317 4959.5
## - lunch_type_free.reduced 1 26383.6 189314 5065.4
##
## Step: AIC=4923.26
## math_score ~ gender_male + ethnic_group_B + ethnic_group_C +
## ethnic_group_D + ethnic_group_E + parent_educ_some.college +
## parent_educ_associate.s.degree + parent_educ_bachelor.s.degree +
## parent_educ_master.s.degree + lunch_type_free.reduced + test_prep_completed +
## parent_marital_status_divorced + parent_marital_status_single +
## practice_sport_sometimes + practice_sport_regularly + is_first_child_yes +
## transport_means_private + nr_siblings_1 + nr_siblings_2 +
## wkly_study_hours_..10.hours + wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group_C 1 58.9 163018 4921.6
## - ethnic_group_B 1 87.6 163046 4921.8
## - transport_means_private 1 93.5 163052 4921.8
## - nr_siblings_2 1 180.1 163139 4922.3
## - nr_siblings_1 1 334.9 163294 4923.2
## <none> 162959 4923.3
## - practice_sport_sometimes 1 419.0 163378 4923.7
## - practice_sport_regularly 1 901.2 163860 4926.5
## - is_first_child_yes 1 1017.1 163976 4927.2
## - wkly_study_hours_..10.hours 1 1274.6 164233 4928.6
## - parent_marital_status_single 1 1348.3 164307 4929.1
## - ethnic_group_D 1 1453.8 164413 4929.7
## - wkly_study_hours_5.10.hours 1 1583.4 164542 4930.4
## - parent_marital_status_divorced 1 1875.1 164834 4932.1
## - parent_educ_some.college 1 2108.2 165067 4933.4
## - parent_educ_master.s.degree 1 2978.4 165937 4938.4
## - parent_educ_associate.s.degree 1 3030.4 165989 4938.7
## - parent_educ_bachelor.s.degree 1 3146.8 166106 4939.4
## - ethnic_group_E 1 4378.6 167337 4946.4
## - gender_male 1 5690.7 168649 4953.8
## - test_prep_completed 1 6540.7 169499 4958.6
## - lunch_type_free.reduced 1 26390.1 189349 5063.5
##
## Step: AIC=4921.6
## math_score ~ gender_male + ethnic_group_B + ethnic_group_D +
## ethnic_group_E + parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + practice_sport_sometimes +
## practice_sport_regularly + is_first_child_yes + transport_means_private +
## nr_siblings_1 + nr_siblings_2 + wkly_study_hours_..10.hours +
## wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group_B 1 30.3 163048 4919.8
## - transport_means_private 1 84.5 163102 4920.1
## - nr_siblings_2 1 185.5 163203 4920.7
## <none> 163018 4921.6
## - nr_siblings_1 1 344.8 163362 4921.6
## - practice_sport_sometimes 1 423.9 163442 4922.1
## - practice_sport_regularly 1 911.0 163929 4924.9
## - is_first_child_yes 1 1023.3 164041 4925.5
## - wkly_study_hours_..10.hours 1 1246.9 164265 4926.8
## - parent_marital_status_single 1 1356.1 164374 4927.5
## - wkly_study_hours_5.10.hours 1 1559.6 164577 4928.6
## - parent_marital_status_divorced 1 1908.0 164926 4930.6
## - parent_educ_some.college 1 2129.8 165147 4931.9
## - ethnic_group_D 1 2480.1 165498 4933.9
## - parent_educ_master.s.degree 1 3015.9 166034 4937.0
## - parent_educ_associate.s.degree 1 3109.9 166128 4937.5
## - parent_educ_bachelor.s.degree 1 3174.4 166192 4937.9
## - gender_male 1 5633.4 168651 4951.8
## - test_prep_completed 1 6545.9 169564 4956.9
## - ethnic_group_E 1 7027.2 170045 4959.6
## - lunch_type_free.reduced 1 26532.7 189550 5062.6
##
## Step: AIC=4919.78
## math_score ~ gender_male + ethnic_group_D + ethnic_group_E +
## parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + practice_sport_sometimes +
## practice_sport_regularly + is_first_child_yes + transport_means_private +
## nr_siblings_1 + nr_siblings_2 + wkly_study_hours_..10.hours +
## wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - transport_means_private 1 89.1 163137 4918.3
## - nr_siblings_2 1 180.1 163228 4918.8
## - nr_siblings_1 1 336.1 163384 4919.7
## <none> 163048 4919.8
## - practice_sport_sometimes 1 421.4 163469 4920.2
## - practice_sport_regularly 1 915.8 163964 4923.1
## - is_first_child_yes 1 1026.8 164075 4923.7
## - wkly_study_hours_..10.hours 1 1234.6 164283 4924.9
## - parent_marital_status_single 1 1352.8 164401 4925.6
## - wkly_study_hours_5.10.hours 1 1537.7 164586 4926.7
## - parent_marital_status_divorced 1 1915.4 164963 4928.8
## - parent_educ_some.college 1 2112.7 165161 4930.0
## - ethnic_group_D 1 2615.9 165664 4932.9
## - parent_educ_master.s.degree 1 2995.1 166043 4935.0
## - parent_educ_associate.s.degree 1 3101.6 166150 4935.6
## - parent_educ_bachelor.s.degree 1 3157.7 166206 4936.0
## - gender_male 1 5629.5 168677 4950.0
## - test_prep_completed 1 6547.1 169595 4955.1
## - ethnic_group_E 1 7350.4 170398 4959.6
## - lunch_type_free.reduced 1 26522.7 189571 5060.7
##
## Step: AIC=4918.3
## math_score ~ gender_male + ethnic_group_D + ethnic_group_E +
## parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + practice_sport_sometimes +
## practice_sport_regularly + is_first_child_yes + nr_siblings_1 +
## nr_siblings_2 + wkly_study_hours_..10.hours + wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - nr_siblings_2 1 182.2 163319 4917.4
## - nr_siblings_1 1 329.3 163466 4918.2
## <none> 163137 4918.3
## - practice_sport_sometimes 1 431.9 163569 4918.8
## - practice_sport_regularly 1 921.6 164059 4921.6
## - is_first_child_yes 1 1029.5 164167 4922.3
## - wkly_study_hours_..10.hours 1 1240.8 164378 4923.5
## - parent_marital_status_single 1 1382.0 164519 4924.3
## - wkly_study_hours_5.10.hours 1 1545.8 164683 4925.2
## - parent_marital_status_divorced 1 1936.4 165073 4927.5
## - parent_educ_some.college 1 2128.6 165266 4928.6
## - ethnic_group_D 1 2614.3 165751 4931.4
## - parent_educ_master.s.degree 1 2994.4 166131 4933.5
## - parent_educ_bachelor.s.degree 1 3192.1 166329 4934.7
## - parent_educ_associate.s.degree 1 3212.9 166350 4934.8
## - gender_male 1 5615.4 168752 4948.4
## - test_prep_completed 1 6513.8 169651 4953.4
## - ethnic_group_E 1 7372.3 170509 4958.2
## - lunch_type_free.reduced 1 26502.3 189639 5059.0
##
## Step: AIC=4917.35
## math_score ~ gender_male + ethnic_group_D + ethnic_group_E +
## parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + practice_sport_sometimes +
## practice_sport_regularly + is_first_child_yes + nr_siblings_1 +
## wkly_study_hours_..10.hours + wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - nr_siblings_1 1 205.5 163525 4916.5
## <none> 163319 4917.4
## - practice_sport_sometimes 1 459.5 163779 4918.0
## - practice_sport_regularly 1 933.5 164253 4920.8
## - is_first_child_yes 1 1137.9 164457 4921.9
## - wkly_study_hours_..10.hours 1 1240.5 164560 4922.5
## - parent_marital_status_single 1 1399.3 164718 4923.4
## - wkly_study_hours_5.10.hours 1 1544.0 164863 4924.3
## - parent_marital_status_divorced 1 1912.6 165232 4926.4
## - parent_educ_some.college 1 2120.6 165440 4927.6
## - ethnic_group_D 1 2631.4 165951 4930.5
## - parent_educ_master.s.degree 1 2919.9 166239 4932.2
## - parent_educ_bachelor.s.degree 1 3206.8 166526 4933.8
## - parent_educ_associate.s.degree 1 3239.1 166558 4934.0
## - gender_male 1 5633.0 168952 4947.5
## - test_prep_completed 1 6522.2 169841 4952.5
## - ethnic_group_E 1 7552.9 170872 4958.2
## - lunch_type_free.reduced 1 26680.5 190000 5058.8
##
## Step: AIC=4916.55
## math_score ~ gender_male + ethnic_group_D + ethnic_group_E +
## parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + practice_sport_sometimes +
## practice_sport_regularly + is_first_child_yes + wkly_study_hours_..10.hours +
## wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## <none> 163525 4916.5
## - practice_sport_sometimes 1 488.3 164013 4917.4
## - practice_sport_regularly 1 965.0 164490 4920.1
## - is_first_child_yes 1 1164.6 164689 4921.3
## - wkly_study_hours_..10.hours 1 1246.0 164771 4921.7
## - parent_marital_status_single 1 1396.5 164921 4922.6
## - wkly_study_hours_5.10.hours 1 1540.6 165065 4923.4
## - parent_marital_status_divorced 1 1941.9 165467 4925.7
## - parent_educ_some.college 1 2106.7 165631 4926.7
## - ethnic_group_D 1 2698.3 166223 4930.1
## - parent_educ_master.s.degree 1 2824.9 166350 4930.8
## - parent_educ_associate.s.degree 1 3197.7 166722 4932.9
## - parent_educ_bachelor.s.degree 1 3215.7 166740 4933.0
## - gender_male 1 5672.4 169197 4946.9
## - test_prep_completed 1 6538.1 170063 4951.7
## - ethnic_group_E 1 7669.8 171195 4958.0
## - lunch_type_free.reduced 1 26633.4 190158 5057.6aic_step_math = AIC(lm_step_math)
bic_step_math = BIC(lm_step_math)
adjr2_step_math = lm_step_math |> broom::glance() |> pull(adj.r.squared)Reading
lm_step_reading = stepAIC(lm_all_reading, direction = "backward")## Start: AIC=4888.54
## reading_score ~ gender_male + ethnic_group_B + ethnic_group_C +
## ethnic_group_D + ethnic_group_E + parent_educ_high.school +
## parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + parent_marital_status_widowed +
## practice_sport_sometimes + practice_sport_regularly + is_first_child_yes +
## transport_means_private + nr_siblings_1 + nr_siblings_2 +
## nr_siblings_3 + nr_siblings_4. + wkly_study_hours_..10.hours +
## wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - parent_marital_status_widowed 1 0.0 155779 4886.5
## - nr_siblings_4. 1 0.0 155779 4886.5
## - nr_siblings_3 1 4.5 155784 4886.6
## - ethnic_group_B 1 4.8 155784 4886.6
## - nr_siblings_1 1 11.3 155790 4886.6
## - nr_siblings_2 1 18.7 155798 4886.7
## - practice_sport_regularly 1 30.2 155809 4886.7
## - ethnic_group_C 1 30.9 155810 4886.7
## - parent_educ_high.school 1 69.9 155849 4887.0
## - practice_sport_sometimes 1 80.2 155859 4887.0
## <none> 155779 4888.5
## - transport_means_private 1 350.8 156130 4888.7
## - wkly_study_hours_..10.hours 1 391.3 156171 4888.9
## - parent_educ_some.college 1 647.9 156427 4890.5
## - ethnic_group_D 1 756.0 156535 4891.1
## - wkly_study_hours_5.10.hours 1 798.5 156578 4891.4
## - is_first_child_yes 1 1137.3 156916 4893.4
## - ethnic_group_E 1 1198.2 156977 4893.8
## - parent_marital_status_single 1 1350.6 157130 4894.7
## - parent_educ_associate.s.degree 1 1633.6 157413 4896.4
## - parent_marital_status_divorced 1 2019.1 157798 4898.8
## - parent_educ_bachelor.s.degree 1 2083.7 157863 4899.1
## - parent_educ_master.s.degree 1 3406.1 159185 4907.0
## - test_prep_completed 1 9961.7 165741 4945.3
## - lunch_type_free.reduced 1 11987.5 167767 4956.8
## - gender_male 1 12081.1 167860 4957.4
##
## Step: AIC=4886.54
## reading_score ~ gender_male + ethnic_group_B + ethnic_group_C +
## ethnic_group_D + ethnic_group_E + parent_educ_high.school +
## parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + practice_sport_sometimes +
## practice_sport_regularly + is_first_child_yes + transport_means_private +
## nr_siblings_1 + nr_siblings_2 + nr_siblings_3 + nr_siblings_4. +
## wkly_study_hours_..10.hours + wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - nr_siblings_4. 1 0.0 155779 4884.5
## - nr_siblings_3 1 4.4 155784 4884.6
## - ethnic_group_B 1 4.8 155784 4884.6
## - nr_siblings_1 1 11.2 155790 4884.6
## - nr_siblings_2 1 18.7 155798 4884.7
## - practice_sport_regularly 1 30.2 155809 4884.7
## - ethnic_group_C 1 30.9 155810 4884.7
## - parent_educ_high.school 1 70.0 155849 4885.0
## - practice_sport_sometimes 1 80.3 155860 4885.0
## <none> 155779 4886.5
## - transport_means_private 1 351.2 156130 4886.7
## - wkly_study_hours_..10.hours 1 391.3 156171 4886.9
## - parent_educ_some.college 1 647.8 156427 4888.5
## - ethnic_group_D 1 757.4 156537 4889.1
## - wkly_study_hours_5.10.hours 1 800.1 156579 4889.4
## - is_first_child_yes 1 1137.8 156917 4891.4
## - ethnic_group_E 1 1198.3 156978 4891.8
## - parent_marital_status_single 1 1367.1 157146 4892.8
## - parent_educ_associate.s.degree 1 1636.3 157416 4894.5
## - parent_marital_status_divorced 1 2037.7 157817 4896.9
## - parent_educ_bachelor.s.degree 1 2083.7 157863 4897.1
## - parent_educ_master.s.degree 1 3407.1 159186 4905.1
## - test_prep_completed 1 9970.2 165749 4943.4
## - lunch_type_free.reduced 1 11989.3 167769 4954.8
## - gender_male 1 12081.9 167861 4955.4
##
## Step: AIC=4884.55
## reading_score ~ gender_male + ethnic_group_B + ethnic_group_C +
## ethnic_group_D + ethnic_group_E + parent_educ_high.school +
## parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + practice_sport_sometimes +
## practice_sport_regularly + is_first_child_yes + transport_means_private +
## nr_siblings_1 + nr_siblings_2 + nr_siblings_3 + wkly_study_hours_..10.hours +
## wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group_B 1 4.8 155784 4882.6
## - nr_siblings_3 1 6.7 155786 4882.6
## - nr_siblings_1 1 18.6 155798 4882.7
## - practice_sport_regularly 1 30.1 155809 4882.7
## - ethnic_group_C 1 30.8 155810 4882.7
## - nr_siblings_2 1 34.4 155814 4882.8
## - parent_educ_high.school 1 70.0 155849 4883.0
## - practice_sport_sometimes 1 80.3 155860 4883.0
## <none> 155779 4884.5
## - transport_means_private 1 351.7 156131 4884.7
## - wkly_study_hours_..10.hours 1 394.4 156174 4884.9
## - parent_educ_some.college 1 650.3 156430 4886.5
## - ethnic_group_D 1 757.9 156537 4887.1
## - wkly_study_hours_5.10.hours 1 802.8 156582 4887.4
## - is_first_child_yes 1 1182.7 156962 4889.7
## - ethnic_group_E 1 1198.9 156978 4889.8
## - parent_marital_status_single 1 1367.2 157146 4890.8
## - parent_educ_associate.s.degree 1 1639.6 157419 4892.5
## - parent_marital_status_divorced 1 2038.3 157818 4894.9
## - parent_educ_bachelor.s.degree 1 2083.7 157863 4895.1
## - parent_educ_master.s.degree 1 3415.8 159195 4903.1
## - test_prep_completed 1 9971.6 165751 4941.4
## - lunch_type_free.reduced 1 12003.6 167783 4952.9
## - gender_male 1 12153.7 167933 4953.8
##
## Step: AIC=4882.57
## reading_score ~ gender_male + ethnic_group_C + ethnic_group_D +
## ethnic_group_E + parent_educ_high.school + parent_educ_some.college +
## parent_educ_associate.s.degree + parent_educ_bachelor.s.degree +
## parent_educ_master.s.degree + lunch_type_free.reduced + test_prep_completed +
## parent_marital_status_divorced + parent_marital_status_single +
## practice_sport_sometimes + practice_sport_regularly + is_first_child_yes +
## transport_means_private + nr_siblings_1 + nr_siblings_2 +
## nr_siblings_3 + wkly_study_hours_..10.hours + wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - nr_siblings_3 1 7.2 155791 4880.6
## - nr_siblings_1 1 19.1 155803 4880.7
## - practice_sport_regularly 1 30.7 155815 4880.8
## - ethnic_group_C 1 33.4 155817 4880.8
## - nr_siblings_2 1 33.8 155818 4880.8
## - parent_educ_high.school 1 68.9 155853 4881.0
## - practice_sport_sometimes 1 80.4 155864 4881.1
## <none> 155784 4882.6
## - transport_means_private 1 350.5 156135 4882.7
## - wkly_study_hours_..10.hours 1 390.2 156174 4882.9
## - parent_educ_some.college 1 651.6 156436 4884.5
## - wkly_study_hours_5.10.hours 1 798.0 156582 4885.4
## - is_first_child_yes 1 1186.1 156970 4887.8
## - ethnic_group_D 1 1364.1 157148 4888.8
## - parent_marital_status_single 1 1367.7 157152 4888.9
## - parent_educ_associate.s.degree 1 1654.1 157438 4890.6
## - ethnic_group_E 1 1871.7 157656 4891.9
## - parent_marital_status_divorced 1 2050.5 157835 4893.0
## - parent_educ_bachelor.s.degree 1 2086.6 157871 4893.2
## - parent_educ_master.s.degree 1 3418.3 159202 4901.2
## - test_prep_completed 1 9975.6 165760 4939.4
## - lunch_type_free.reduced 1 12023.7 167808 4951.1
## - gender_male 1 12236.3 168020 4952.3
##
## Step: AIC=4880.62
## reading_score ~ gender_male + ethnic_group_C + ethnic_group_D +
## ethnic_group_E + parent_educ_high.school + parent_educ_some.college +
## parent_educ_associate.s.degree + parent_educ_bachelor.s.degree +
## parent_educ_master.s.degree + lunch_type_free.reduced + test_prep_completed +
## parent_marital_status_divorced + parent_marital_status_single +
## practice_sport_sometimes + practice_sport_regularly + is_first_child_yes +
## transport_means_private + nr_siblings_1 + nr_siblings_2 +
## wkly_study_hours_..10.hours + wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - nr_siblings_1 1 12.4 155804 4878.7
## - practice_sport_regularly 1 30.6 155822 4878.8
## - ethnic_group_C 1 33.1 155824 4878.8
## - nr_siblings_2 1 63.9 155855 4879.0
## - parent_educ_high.school 1 70.1 155861 4879.0
## - practice_sport_sometimes 1 80.0 155871 4879.1
## <none> 155791 4880.6
## - transport_means_private 1 350.2 156142 4880.7
## - wkly_study_hours_..10.hours 1 393.6 156185 4881.0
## - parent_educ_some.college 1 655.0 156446 4882.6
## - wkly_study_hours_5.10.hours 1 793.8 156585 4883.4
## - is_first_child_yes 1 1182.1 156973 4885.8
## - ethnic_group_D 1 1363.2 157154 4886.9
## - parent_marital_status_single 1 1365.3 157157 4886.9
## - parent_educ_associate.s.degree 1 1654.3 157446 4888.6
## - ethnic_group_E 1 1868.5 157660 4889.9
## - parent_marital_status_divorced 1 2045.2 157836 4891.0
## - parent_educ_bachelor.s.degree 1 2092.5 157884 4891.3
## - parent_educ_master.s.degree 1 3430.3 159222 4899.3
## - test_prep_completed 1 9969.5 165761 4937.4
## - lunch_type_free.reduced 1 12018.7 167810 4949.1
## - gender_male 1 12287.4 168079 4950.6
##
## Step: AIC=4878.69
## reading_score ~ gender_male + ethnic_group_C + ethnic_group_D +
## ethnic_group_E + parent_educ_high.school + parent_educ_some.college +
## parent_educ_associate.s.degree + parent_educ_bachelor.s.degree +
## parent_educ_master.s.degree + lunch_type_free.reduced + test_prep_completed +
## parent_marital_status_divorced + parent_marital_status_single +
## practice_sport_sometimes + practice_sport_regularly + is_first_child_yes +
## transport_means_private + nr_siblings_2 + wkly_study_hours_..10.hours +
## wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - practice_sport_regularly 1 29.2 155833 4876.9
## - ethnic_group_C 1 30.9 155835 4876.9
## - parent_educ_high.school 1 69.8 155873 4877.1
## - practice_sport_sometimes 1 76.7 155880 4877.2
## - nr_siblings_2 1 97.1 155901 4877.3
## <none> 155804 4878.7
## - transport_means_private 1 352.5 156156 4878.8
## - wkly_study_hours_..10.hours 1 392.8 156196 4879.1
## - parent_educ_some.college 1 657.8 156461 4880.7
## - wkly_study_hours_5.10.hours 1 794.6 156598 4881.5
## - is_first_child_yes 1 1171.6 156975 4883.8
## - ethnic_group_D 1 1352.0 157156 4884.9
## - parent_marital_status_single 1 1364.4 157168 4885.0
## - parent_educ_associate.s.degree 1 1660.8 157464 4886.7
## - ethnic_group_E 1 1856.2 157660 4887.9
## - parent_marital_status_divorced 1 2041.4 157845 4889.0
## - parent_educ_bachelor.s.degree 1 2091.3 157895 4889.3
## - parent_educ_master.s.degree 1 3491.2 159295 4897.7
## - test_prep_completed 1 9965.3 165769 4935.5
## - lunch_type_free.reduced 1 12018.9 167823 4947.1
## - gender_male 1 12311.0 168115 4948.8
##
## Step: AIC=4876.87
## reading_score ~ gender_male + ethnic_group_C + ethnic_group_D +
## ethnic_group_E + parent_educ_high.school + parent_educ_some.college +
## parent_educ_associate.s.degree + parent_educ_bachelor.s.degree +
## parent_educ_master.s.degree + lunch_type_free.reduced + test_prep_completed +
## parent_marital_status_divorced + parent_marital_status_single +
## practice_sport_sometimes + is_first_child_yes + transport_means_private +
## nr_siblings_2 + wkly_study_hours_..10.hours + wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group_C 1 31.2 155864 4875.1
## - practice_sport_sometimes 1 52.9 155886 4875.2
## - parent_educ_high.school 1 64.4 155897 4875.3
## - nr_siblings_2 1 97.1 155930 4875.5
## <none> 155833 4876.9
## - transport_means_private 1 355.2 156188 4877.0
## - wkly_study_hours_..10.hours 1 397.8 156231 4877.3
## - parent_educ_some.college 1 668.5 156501 4878.9
## - wkly_study_hours_5.10.hours 1 795.7 156629 4879.7
## - is_first_child_yes 1 1159.4 156992 4881.9
## - parent_marital_status_single 1 1351.9 157185 4883.1
## - ethnic_group_D 1 1356.1 157189 4883.1
## - parent_educ_associate.s.degree 1 1670.6 157503 4885.0
## - ethnic_group_E 1 1842.5 157675 4886.0
## - parent_marital_status_divorced 1 2058.1 157891 4887.3
## - parent_educ_bachelor.s.degree 1 2101.2 157934 4887.6
## - parent_educ_master.s.degree 1 3465.9 159299 4895.7
## - test_prep_completed 1 9994.2 165827 4933.8
## - lunch_type_free.reduced 1 11989.7 167823 4945.1
## - gender_male 1 12320.8 168154 4947.0
##
## Step: AIC=4875.06
## reading_score ~ gender_male + ethnic_group_D + ethnic_group_E +
## parent_educ_high.school + parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + practice_sport_sometimes +
## is_first_child_yes + transport_means_private + nr_siblings_2 +
## wkly_study_hours_..10.hours + wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - practice_sport_sometimes 1 55.2 155919 4873.4
## - parent_educ_high.school 1 62.7 155927 4873.4
## - nr_siblings_2 1 100.2 155964 4873.7
## <none> 155864 4875.1
## - transport_means_private 1 341.4 156205 4875.1
## - wkly_study_hours_..10.hours 1 394.7 156259 4875.5
## - parent_educ_some.college 1 685.3 156549 4877.2
## - wkly_study_hours_5.10.hours 1 801.4 156665 4877.9
## - is_first_child_yes 1 1160.8 157025 4880.1
## - parent_marital_status_single 1 1358.1 157222 4881.3
## - ethnic_group_D 1 1548.1 157412 4882.4
## - parent_educ_associate.s.degree 1 1705.4 157569 4883.4
## - ethnic_group_E 1 1995.6 157860 4885.1
## - parent_marital_status_divorced 1 2069.3 157933 4885.6
## - parent_educ_bachelor.s.degree 1 2130.9 157995 4885.9
## - parent_educ_master.s.degree 1 3515.6 159380 4894.2
## - test_prep_completed 1 9999.2 165863 4932.0
## - lunch_type_free.reduced 1 12040.8 167905 4943.6
## - gender_male 1 12425.5 168290 4945.8
##
## Step: AIC=4873.4
## reading_score ~ gender_male + ethnic_group_D + ethnic_group_E +
## parent_educ_high.school + parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + is_first_child_yes + transport_means_private +
## nr_siblings_2 + wkly_study_hours_..10.hours + wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - parent_educ_high.school 1 61.3 155981 4871.8
## - nr_siblings_2 1 106.9 156026 4872.0
## <none> 155919 4873.4
## - transport_means_private 1 349.7 156269 4873.5
## - wkly_study_hours_..10.hours 1 404.0 156323 4873.8
## - parent_educ_some.college 1 679.3 156599 4875.5
## - wkly_study_hours_5.10.hours 1 808.4 156728 4876.3
## - is_first_child_yes 1 1148.7 157068 4878.4
## - parent_marital_status_single 1 1366.3 157286 4879.7
## - ethnic_group_D 1 1553.6 157473 4880.8
## - parent_educ_associate.s.degree 1 1693.5 157613 4881.6
## - ethnic_group_E 1 1964.6 157884 4883.3
## - parent_marital_status_divorced 1 2067.3 157987 4883.9
## - parent_educ_bachelor.s.degree 1 2152.0 158071 4884.4
## - parent_educ_master.s.degree 1 3556.7 159476 4892.8
## - test_prep_completed 1 10006.5 165926 4930.4
## - lunch_type_free.reduced 1 12034.2 167954 4941.9
## - gender_male 1 12438.8 168358 4944.2
##
## Step: AIC=4871.77
## reading_score ~ gender_male + ethnic_group_D + ethnic_group_E +
## parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + is_first_child_yes + transport_means_private +
## nr_siblings_2 + wkly_study_hours_..10.hours + wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - nr_siblings_2 1 106.0 156087 4870.4
## <none> 155981 4871.8
## - transport_means_private 1 366.3 156347 4872.0
## - wkly_study_hours_..10.hours 1 395.9 156376 4872.2
## - wkly_study_hours_5.10.hours 1 798.1 156779 4874.6
## - is_first_child_yes 1 1128.3 157109 4876.6
## - parent_educ_some.college 1 1287.4 157268 4877.6
## - parent_marital_status_single 1 1344.3 157325 4877.9
## - ethnic_group_D 1 1589.1 157570 4879.4
## - ethnic_group_E 1 1970.3 157951 4881.7
## - parent_marital_status_divorced 1 2058.7 158039 4882.2
## - parent_educ_associate.s.degree 1 2866.3 158847 4887.0
## - parent_educ_bachelor.s.degree 1 3118.9 159099 4888.5
## - parent_educ_master.s.degree 1 4479.0 160460 4896.6
## - test_prep_completed 1 10265.9 166246 4930.2
## - lunch_type_free.reduced 1 12043.9 168024 4940.3
## - gender_male 1 12517.1 168498 4942.9
##
## Step: AIC=4870.41
## reading_score ~ gender_male + ethnic_group_D + ethnic_group_E +
## parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + is_first_child_yes + transport_means_private +
## wkly_study_hours_..10.hours + wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## <none> 156087 4870.4
## - transport_means_private 1 373.4 156460 4870.7
## - wkly_study_hours_..10.hours 1 395.5 156482 4870.8
## - wkly_study_hours_5.10.hours 1 798.1 156885 4873.2
## - is_first_child_yes 1 1201.8 157288 4875.7
## - parent_educ_some.college 1 1284.6 157371 4876.2
## - parent_marital_status_single 1 1357.2 157444 4876.6
## - ethnic_group_D 1 1586.7 157673 4878.0
## - ethnic_group_E 1 2013.8 158100 4880.6
## - parent_marital_status_divorced 1 2034.3 158121 4880.7
## - parent_educ_associate.s.degree 1 2892.1 158979 4885.8
## - parent_educ_bachelor.s.degree 1 3127.8 159214 4887.2
## - parent_educ_master.s.degree 1 4444.5 160531 4895.0
## - test_prep_completed 1 10269.5 166356 4928.8
## - lunch_type_free.reduced 1 12138.7 168225 4939.4
## - gender_male 1 12513.2 168600 4941.5aic_step_reading = AIC(lm_step_reading)
bic_step_reading = BIC(lm_step_reading)
adjr2_step_reading = lm_step_reading |> broom::glance() |> pull(adj.r.squared)Writing
lm_step_writing = stepAIC(lm_all_writing, direction = "backward")## Start: AIC=4835.37
## writing_score ~ gender_male + ethnic_group_B + ethnic_group_C +
## ethnic_group_D + ethnic_group_E + parent_educ_high.school +
## parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + parent_marital_status_widowed +
## practice_sport_sometimes + practice_sport_regularly + is_first_child_yes +
## transport_means_private + nr_siblings_1 + nr_siblings_2 +
## nr_siblings_3 + nr_siblings_4. + wkly_study_hours_..10.hours +
## wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - nr_siblings_4. 1 0.1 147282 4833.4
## - nr_siblings_3 1 0.5 147282 4833.4
## - ethnic_group_B 1 1.7 147283 4833.4
## - parent_marital_status_widowed 1 20.1 147302 4833.5
## - nr_siblings_1 1 26.0 147308 4833.5
## - parent_educ_high.school 1 28.6 147310 4833.6
## - ethnic_group_C 1 40.9 147323 4833.6
## - nr_siblings_2 1 90.9 147373 4834.0
## - transport_means_private 1 266.3 147548 4835.1
## <none> 147282 4835.4
## - wkly_study_hours_..10.hours 1 375.8 147657 4835.8
## - practice_sport_sometimes 1 430.0 147712 4836.1
## - practice_sport_regularly 1 705.2 147987 4837.9
## - wkly_study_hours_5.10.hours 1 795.2 148077 4838.5
## - is_first_child_yes 1 813.1 148095 4838.6
## - ethnic_group_E 1 1003.3 148285 4839.8
## - parent_marital_status_single 1 1649.8 148932 4843.9
## - parent_educ_some.college 1 1683.7 148965 4844.1
## - ethnic_group_D 1 1808.8 149091 4844.9
## - parent_marital_status_divorced 1 2114.6 149396 4846.9
## - parent_educ_associate.s.degree 1 2664.0 149946 4850.4
## - parent_educ_bachelor.s.degree 1 4128.2 151410 4859.6
## - parent_educ_master.s.degree 1 5745.6 153027 4869.6
## - lunch_type_free.reduced 1 14934.9 162217 4924.9
## - test_prep_completed 1 19121.0 166403 4949.1
## - gender_male 1 19504.1 166786 4951.3
##
## Step: AIC=4833.37
## writing_score ~ gender_male + ethnic_group_B + ethnic_group_C +
## ethnic_group_D + ethnic_group_E + parent_educ_high.school +
## parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + parent_marital_status_widowed +
## practice_sport_sometimes + practice_sport_regularly + is_first_child_yes +
## transport_means_private + nr_siblings_1 + nr_siblings_2 +
## nr_siblings_3 + wkly_study_hours_..10.hours + wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - nr_siblings_3 1 1.3 147283 4831.4
## - ethnic_group_B 1 1.8 147284 4831.4
## - parent_marital_status_widowed 1 20.3 147302 4831.5
## - parent_educ_high.school 1 28.9 147311 4831.6
## - ethnic_group_C 1 41.0 147323 4831.6
## - nr_siblings_1 1 43.5 147325 4831.6
## - nr_siblings_2 1 152.7 147435 4832.4
## - transport_means_private 1 266.3 147548 4833.1
## <none> 147282 4833.4
## - wkly_study_hours_..10.hours 1 377.4 147659 4833.8
## - practice_sport_sometimes 1 430.7 147712 4834.1
## - practice_sport_regularly 1 706.8 147989 4835.9
## - wkly_study_hours_5.10.hours 1 796.5 148078 4836.5
## - is_first_child_yes 1 850.5 148132 4836.8
## - ethnic_group_E 1 1004.7 148286 4837.8
## - parent_marital_status_single 1 1651.0 148933 4841.9
## - parent_educ_some.college 1 1687.6 148969 4842.2
## - ethnic_group_D 1 1812.0 149094 4843.0
## - parent_marital_status_divorced 1 2114.6 149396 4844.9
## - parent_educ_associate.s.degree 1 2667.7 149950 4848.4
## - parent_educ_bachelor.s.degree 1 4128.3 151410 4857.6
## - parent_educ_master.s.degree 1 5756.1 153038 4867.7
## - lunch_type_free.reduced 1 14955.9 162238 4923.1
## - test_prep_completed 1 19121.7 166403 4947.1
## - gender_male 1 19610.7 166892 4949.9
##
## Step: AIC=4831.38
## writing_score ~ gender_male + ethnic_group_B + ethnic_group_C +
## ethnic_group_D + ethnic_group_E + parent_educ_high.school +
## parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + parent_marital_status_widowed +
## practice_sport_sometimes + practice_sport_regularly + is_first_child_yes +
## transport_means_private + nr_siblings_1 + nr_siblings_2 +
## wkly_study_hours_..10.hours + wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group_B 1 1.9 147285 4829.4
## - parent_marital_status_widowed 1 20.3 147303 4829.5
## - parent_educ_high.school 1 29.2 147312 4829.6
## - ethnic_group_C 1 41.3 147324 4829.6
## - nr_siblings_1 1 66.5 147350 4829.8
## - nr_siblings_2 1 212.9 147496 4830.7
## - transport_means_private 1 266.2 147549 4831.1
## <none> 147283 4831.4
## - wkly_study_hours_..10.hours 1 379.1 147662 4831.8
## - practice_sport_sometimes 1 430.4 147714 4832.1
## - practice_sport_regularly 1 706.6 147990 4833.9
## - wkly_study_hours_5.10.hours 1 795.2 148078 4834.5
## - is_first_child_yes 1 856.3 148139 4834.9
## - ethnic_group_E 1 1005.7 148289 4835.8
## - parent_marital_status_single 1 1650.0 148933 4839.9
## - parent_educ_some.college 1 1690.5 148974 4840.2
## - ethnic_group_D 1 1815.4 149099 4841.0
## - parent_marital_status_divorced 1 2113.3 149396 4842.9
## - parent_educ_associate.s.degree 1 2667.6 149951 4846.4
## - parent_educ_bachelor.s.degree 1 4132.9 151416 4855.6
## - parent_educ_master.s.degree 1 5765.9 153049 4865.8
## - lunch_type_free.reduced 1 14954.7 162238 4921.1
## - test_prep_completed 1 19121.7 166405 4945.1
## - gender_male 1 19659.2 166942 4948.2
##
## Step: AIC=4829.39
## writing_score ~ gender_male + ethnic_group_C + ethnic_group_D +
## ethnic_group_E + parent_educ_high.school + parent_educ_some.college +
## parent_educ_associate.s.degree + parent_educ_bachelor.s.degree +
## parent_educ_master.s.degree + lunch_type_free.reduced + test_prep_completed +
## parent_marital_status_divorced + parent_marital_status_single +
## parent_marital_status_widowed + practice_sport_sometimes +
## practice_sport_regularly + is_first_child_yes + transport_means_private +
## nr_siblings_1 + nr_siblings_2 + wkly_study_hours_..10.hours +
## wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - parent_marital_status_widowed 1 19.6 147305 4827.5
## - parent_educ_high.school 1 28.8 147314 4827.6
## - ethnic_group_C 1 62.9 147348 4827.8
## - nr_siblings_1 1 66.3 147351 4827.8
## - nr_siblings_2 1 212.5 147498 4828.8
## - transport_means_private 1 265.5 147551 4829.1
## <none> 147285 4829.4
## - wkly_study_hours_..10.hours 1 377.2 147662 4829.8
## - practice_sport_sometimes 1 430.6 147716 4830.2
## - practice_sport_regularly 1 708.4 147993 4831.9
## - wkly_study_hours_5.10.hours 1 794.2 148079 4832.5
## - is_first_child_yes 1 857.5 148143 4832.9
## - ethnic_group_E 1 1610.2 148895 4837.7
## - parent_marital_status_single 1 1649.6 148935 4837.9
## - parent_educ_some.college 1 1692.0 148977 4838.2
## - parent_marital_status_divorced 1 2120.3 149405 4840.9
## - parent_educ_associate.s.degree 1 2684.1 149969 4844.5
## - ethnic_group_D 1 3509.9 150795 4849.7
## - parent_educ_bachelor.s.degree 1 4136.0 151421 4853.6
## - parent_educ_master.s.degree 1 5768.0 153053 4863.8
## - lunch_type_free.reduced 1 14973.4 162258 4919.2
## - test_prep_completed 1 19124.2 166409 4943.1
## - gender_male 1 19772.2 167057 4946.8
##
## Step: AIC=4827.52
## writing_score ~ gender_male + ethnic_group_C + ethnic_group_D +
## ethnic_group_E + parent_educ_high.school + parent_educ_some.college +
## parent_educ_associate.s.degree + parent_educ_bachelor.s.degree +
## parent_educ_master.s.degree + lunch_type_free.reduced + test_prep_completed +
## parent_marital_status_divorced + parent_marital_status_single +
## practice_sport_sometimes + practice_sport_regularly + is_first_child_yes +
## transport_means_private + nr_siblings_1 + nr_siblings_2 +
## wkly_study_hours_..10.hours + wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - parent_educ_high.school 1 29.6 147334 4825.7
## - ethnic_group_C 1 63.9 147369 4825.9
## - nr_siblings_1 1 64.8 147369 4825.9
## - nr_siblings_2 1 208.0 147513 4826.9
## - transport_means_private 1 259.6 147564 4827.2
## <none> 147305 4827.5
## - wkly_study_hours_..10.hours 1 375.7 147680 4827.9
## - practice_sport_sometimes 1 437.0 147742 4828.3
## - practice_sport_regularly 1 704.5 148009 4830.0
## - wkly_study_hours_5.10.hours 1 784.2 148089 4830.5
## - is_first_child_yes 1 854.1 148159 4831.0
## - ethnic_group_E 1 1626.7 148931 4835.9
## - parent_marital_status_single 1 1630.0 148935 4835.9
## - parent_educ_some.college 1 1689.7 148994 4836.3
## - parent_marital_status_divorced 1 2100.7 149405 4838.9
## - parent_educ_associate.s.degree 1 2701.2 150006 4842.7
## - ethnic_group_D 1 3510.1 150815 4847.8
## - parent_educ_bachelor.s.degree 1 4135.6 151440 4851.8
## - parent_educ_master.s.degree 1 5755.8 153060 4861.9
## - lunch_type_free.reduced 1 14988.4 162293 4917.4
## - test_prep_completed 1 19104.6 166409 4941.1
## - gender_male 1 19769.9 167075 4944.9
##
## Step: AIC=4825.71
## writing_score ~ gender_male + ethnic_group_C + ethnic_group_D +
## ethnic_group_E + parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + practice_sport_sometimes +
## practice_sport_regularly + is_first_child_yes + transport_means_private +
## nr_siblings_1 + nr_siblings_2 + wkly_study_hours_..10.hours +
## wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group_C 1 62.2 147396 4824.1
## - nr_siblings_1 1 65.2 147399 4824.1
## - nr_siblings_2 1 207.6 147542 4825.0
## - transport_means_private 1 269.5 147604 4825.4
## <none> 147334 4825.7
## - wkly_study_hours_..10.hours 1 370.6 147705 4826.1
## - practice_sport_sometimes 1 425.5 147760 4826.4
## - practice_sport_regularly 1 689.0 148023 4828.1
## - wkly_study_hours_5.10.hours 1 777.4 148112 4828.7
## - is_first_child_yes 1 841.5 148176 4829.1
## - parent_marital_status_single 1 1613.8 148948 4834.0
## - ethnic_group_E 1 1624.8 148959 4834.1
## - parent_marital_status_divorced 1 2095.8 149430 4837.1
## - parent_educ_some.college 1 2727.9 150062 4841.1
## - ethnic_group_D 1 3535.9 150870 4846.2
## - parent_educ_associate.s.degree 1 4200.6 151535 4850.4
## - parent_educ_bachelor.s.degree 1 5585.0 152919 4859.0
## - parent_educ_master.s.degree 1 6920.2 154254 4867.2
## - lunch_type_free.reduced 1 14992.2 162327 4915.6
## - test_prep_completed 1 19456.0 166790 4941.3
## - gender_male 1 19854.7 167189 4943.6
##
## Step: AIC=4824.11
## writing_score ~ gender_male + ethnic_group_D + ethnic_group_E +
## parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + practice_sport_sometimes +
## practice_sport_regularly + is_first_child_yes + transport_means_private +
## nr_siblings_1 + nr_siblings_2 + wkly_study_hours_..10.hours +
## wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - nr_siblings_1 1 72.8 147469 4822.6
## - nr_siblings_2 1 218.4 147615 4823.5
## - transport_means_private 1 251.7 147648 4823.7
## <none> 147396 4824.1
## - wkly_study_hours_..10.hours 1 366.4 147763 4824.5
## - practice_sport_sometimes 1 431.7 147828 4824.9
## - practice_sport_regularly 1 690.6 148087 4826.5
## - wkly_study_hours_5.10.hours 1 785.6 148182 4827.1
## - is_first_child_yes 1 842.1 148239 4827.5
## - parent_marital_status_single 1 1623.9 149020 4832.5
## - ethnic_group_E 1 1661.6 149058 4832.7
## - parent_marital_status_divorced 1 2110.7 149507 4835.6
## - parent_educ_some.college 1 2774.8 150171 4839.8
## - ethnic_group_D 1 4133.8 151530 4848.3
## - parent_educ_associate.s.degree 1 4279.4 151676 4849.2
## - parent_educ_bachelor.s.degree 1 5646.9 153043 4857.7
## - parent_educ_master.s.degree 1 7022.2 154419 4866.2
## - lunch_type_free.reduced 1 15069.3 162466 4914.4
## - test_prep_completed 1 19460.1 166857 4939.7
## - gender_male 1 20037.5 167434 4942.9
##
## Step: AIC=4822.58
## writing_score ~ gender_male + ethnic_group_D + ethnic_group_E +
## parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + practice_sport_sometimes +
## practice_sport_regularly + is_first_child_yes + transport_means_private +
## nr_siblings_2 + wkly_study_hours_..10.hours + wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - nr_siblings_2 1 158.5 147628 4821.6
## - transport_means_private 1 246.3 147716 4822.2
## <none> 147469 4822.6
## - wkly_study_hours_..10.hours 1 368.1 147837 4822.9
## - practice_sport_sometimes 1 454.3 147924 4823.5
## - practice_sport_regularly 1 708.5 148178 4825.1
## - wkly_study_hours_5.10.hours 1 784.0 148253 4825.6
## - is_first_child_yes 1 876.8 148346 4826.2
## - parent_marital_status_single 1 1626.8 149096 4831.0
## - ethnic_group_E 1 1711.1 149180 4831.5
## - parent_marital_status_divorced 1 2122.4 149592 4834.1
## - parent_educ_some.college 1 2764.5 150234 4838.2
## - ethnic_group_D 1 4189.7 151659 4847.1
## - parent_educ_associate.s.degree 1 4261.0 151730 4847.6
## - parent_educ_bachelor.s.degree 1 5658.8 153128 4856.3
## - parent_educ_master.s.degree 1 6951.0 154420 4864.2
## - lunch_type_free.reduced 1 15072.7 162542 4912.8
## - test_prep_completed 1 19478.1 166947 4938.2
## - gender_male 1 19998.7 167468 4941.1
##
## Step: AIC=4821.59
## writing_score ~ gender_male + ethnic_group_D + ethnic_group_E +
## parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + practice_sport_sometimes +
## practice_sport_regularly + is_first_child_yes + transport_means_private +
## wkly_study_hours_..10.hours + wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## - transport_means_private 1 252.9 147881 4821.2
## <none> 147628 4821.6
## - wkly_study_hours_..10.hours 1 366.9 147995 4821.9
## - practice_sport_sometimes 1 469.7 148098 4822.6
## - practice_sport_regularly 1 709.3 148337 4824.1
## - wkly_study_hours_5.10.hours 1 783.5 148411 4824.6
## - is_first_child_yes 1 954.5 148582 4825.7
## - parent_marital_status_single 1 1643.5 149271 4830.1
## - ethnic_group_E 1 1762.6 149390 4830.8
## - parent_marital_status_divorced 1 2091.9 149720 4832.9
## - parent_educ_some.college 1 2760.9 150389 4837.2
## - ethnic_group_D 1 4184.3 151812 4846.1
## - parent_educ_associate.s.degree 1 4302.0 151930 4846.8
## - parent_educ_bachelor.s.degree 1 5671.4 153299 4855.3
## - parent_educ_master.s.degree 1 6896.1 154524 4862.9
## - lunch_type_free.reduced 1 15201.3 162829 4912.5
## - test_prep_completed 1 19483.7 167112 4937.1
## - gender_male 1 19991.4 167619 4940.0
##
## Step: AIC=4821.22
## writing_score ~ gender_male + ethnic_group_D + ethnic_group_E +
## parent_educ_some.college + parent_educ_associate.s.degree +
## parent_educ_bachelor.s.degree + parent_educ_master.s.degree +
## lunch_type_free.reduced + test_prep_completed + parent_marital_status_divorced +
## parent_marital_status_single + practice_sport_sometimes +
## practice_sport_regularly + is_first_child_yes + wkly_study_hours_..10.hours +
## wkly_study_hours_5.10.hours
##
## Df Sum of Sq RSS AIC
## <none> 147881 4821.2
## - wkly_study_hours_..10.hours 1 372.5 148253 4821.6
## - practice_sport_sometimes 1 487.8 148368 4822.3
## - practice_sport_regularly 1 717.3 148598 4823.8
## - wkly_study_hours_5.10.hours 1 793.3 148674 4824.3
## - is_first_child_yes 1 959.0 148840 4825.3
## - parent_marital_status_single 1 1696.8 149578 4830.0
## - ethnic_group_E 1 1779.3 149660 4830.6
## - parent_marital_status_divorced 1 2127.1 150008 4832.8
## - parent_educ_some.college 1 2791.6 150672 4836.9
## - ethnic_group_D 1 4179.2 152060 4845.6
## - parent_educ_associate.s.degree 1 4512.6 152393 4847.7
## - parent_educ_bachelor.s.degree 1 5747.7 153628 4855.4
## - parent_educ_master.s.degree 1 6897.6 154778 4862.4
## - lunch_type_free.reduced 1 15176.2 163057 4911.8
## - test_prep_completed 1 19386.8 167267 4936.0
## - gender_male 1 20042.2 167923 4939.7aic_step_writing = AIC(lm_step_writing)
bic_step_writing = BIC(lm_step_writing)
adjr2_step_writing = lm_step_writing |> broom::glance() |> pull(adj.r.squared)Readable Tables of Results
Math
model_stats_math = tibble(
math_model_type = c("All", "Backward Selection", "Economic", "Hard Worker", "Demographic", "Family Structure"),
ADJ_R2 = c(adjr2_all_math,
adjr2_step_math,
adjr2_econ_math,
adjr2_hw_math,
adjr2_demo_math,
adjr2_fam_math),
AIC = c(aic_all_math,
aic_step_math,
aic_econ_math,
aic_hw_math,
aic_demo_math,
aic_fam_math),
BIC = c(bic_all_math,
bic_step_math,
bic_econ_math,
bic_hw_math,
bic_demo_math,
bic_fam_math)
)
model_stats_math |> knitr::kable()| math_model_type | ADJ_R2 | AIC | BIC |
|---|---|---|---|
| All | 0.2673613 | 7623.361 | 7754.429 |
| Backward Selection | 0.271766 | 7608.853 | 7696.231 |
| Economic | 0.1853197 | 7707.305 | 7755.848 |
| Hard Worker | 0.01053602 | 7887.595 | 7916.721 |
| Demographic | 0.07677012 | 7822.907 | 7856.887 |
| Family Structure | 0.01569303 | 7886.611 | 7935.155 |
Reading
model_stats_reading = tibble(
reading_model_type = c("All", "Backward Selection", "Economic", "Hard Worker", "Demographic", "Family Structure"),
ADJ_R2 = c(adjr2_all_reading,
adjr2_step_reading,
adjr2_econ_reading,
adjr2_hw_reading,
adjr2_demo_reading,
adjr2_fam_reading),
AIC = c(aic_all_reading,
aic_step_reading,
aic_econ_reading,
aic_hw_reading,
aic_demo_reading,
aic_fam_reading),
BIC = c(bic_all_reading,
bic_step_reading,
bic_econ_reading,
bic_hw_reading,
bic_demo_reading,
bic_fam_reading)
)
model_stats_reading |> knitr::kable()| reading_model_type | ADJ_R2 | AIC | BIC |
|---|---|---|---|
| All | 0.2286039 | 7580.852 | 7711.920 |
| Backward Selection | 0.2353751 | 7562.721 | 7645.245 |
| Economic | 0.1474199 | 7659.034 | 7707.578 |
| Hard Worker | 0.002965035 | 7803.444 | 7832.570 |
| Demographic | 0.07241858 | 7735.987 | 7769.968 |
| Family Structure | 0.01454485 | 7796.339 | 7844.883 |
Writing
model_stats_writing = tibble(
writing_model_type = c("All", "Backward Selection", "Economic", "Hard Worker", "Demographic", "Family Structure"),
ADJ_R2 = c(adjr2_all_writing,
adjr2_step_writing,
adjr2_econ_writing,
adjr2_hw_writing,
adjr2_demo_writing,
adjr2_fam_writing),
AIC = c(aic_all_writing,
aic_step_writing,
aic_econ_writing,
aic_hw_writing,
aic_demo_writing,
aic_fam_writing),
BIC = c(bic_all_writing,
bic_step_writing,
bic_econ_writing,
bic_hw_writing,
bic_demo_writing,
bic_fam_writing)
)
model_stats_writing |> knitr::kable()| writing_model_type | ADJ_R2 | AIC | BIC |
|---|---|---|---|
| All | 0.3275407 | 7527.677 | 7658.744 |
| Backward Selection | 0.3313331 | 7513.524 | 7600.902 |
| Economic | 0.2084674 | 7665.549 | 7714.092 |
| Hard Worker | 0.003411755 | 7879.966 | 7909.092 |
| Demographic | 0.1072178 | 7776.685 | 7810.666 |
| Family Structure | 0.01292108 | 7874.847 | 7923.391 |
Final model statistics
t1 <- broom::tidy(lm_step_math) |> dplyr::select(-std.error)
t2 <- broom::tidy(lm_step_reading) |> dplyr::select(-std.error)
t3 <- broom::tidy(lm_step_writing) |> dplyr::select(-std.error)Model Diagnostics
Plotting the residuals against the fitted values, we see no significant relationship.
plot(predict(lm_all_math, score_dummies), lm_all_math$residuals)
Examining the residuals for normality, we see some deviation, but not egregious deviation.
qqnorm(lm_all_math$residuals)
Examining the residuals versus leverage, we find that no point is exerting fully undue leverage.
plot(lm_all_math, which = 5)